A remark on asymptotic of highest weights in tensor powers of a representation

Details A remark on asymptotic of highest weights in tensor powers of a representation A remark on asymptotic of highest weights in tensor powers of a representation

2010-02-09

arxiv.org/abs/1002.1984v1

Mathematics

Representation Theory

7 pages

Scientific paper

We consider the semigroup S of highest weights appearing in tensor powers V^k of a finite dimensional representation V of a connected reductive group. We describe the cone generated by S as the cone over the weight polytope of V intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in V^k in terms of the volume of this polytope.

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